Here, \(u\)  is the complex-valued slowly varying envelope of the electric field of the optical beam and \(\theta \)  is the
extra optically induced rotation of the director beyond the imposed pre-tilt \(\theta _{0}\) . The parameter \(q\)  is
proportional to the square of the imposed pre-tilting electric field and \(\nu \)  is the non-dimensional elasticity
of the nematic. The electric field equation (REF ) is a defocusing NLS-type equation and the director equation
() is forced by the intensity of the electric field. Note that the nematic equations describe bulk waves,
including bulk solitary waves, as \(z\)  is a spatial coordinate, even though it is “time-like” in the context of the
NLS-type equation (REF ). For typical experimental conditions \(\nu = O(100)\) 
[1]}, [2]}, [3]}, [4]}. In this limit the nematic response is termed non-local in the sense that
the response of the nematic to the optical forcing extends far beyond the waist of the optical beam [5]}, [6]}, [7]}.
This nonlocal response and large value of \(\nu \)  will play a dominating role in the variety of structures possible for the
DSW solution of the nematic equations (REF ) and (). We note that in the so-called local limit
\(\nu \rightarrow 0\) , the nematic equations (REF ) and () reduce to the defocusing NLS equation, whose DSW
solution is known [8]}. While the nematic equations are of NLS-type, the nematic DSW more resembles a KdV DSW
[9]}, [10]} than an NLS DSW [8]} due to the large nonlocality \(\nu \) .
